Solution:

Number of ways to go from A to B = 6
Number of ways to return from B to A = 6
Total number of ways to go from A to B and return = 6 x 6 = 36

Explanation:

To understand this problem, we need to understand the concept of permutations and combinations. Permutations are the number of ways in which we can arrange a set of objects in a specific order, while combinations are the number of ways in which we can select a subset of objects from a larger set without regard to order.

In this problem, we need to find the total number of ways in which we can go from station A to station B and return, given that there are 6 different routes from A to B and we can choose any of these routes for returning.

We can solve this problem by using the multiplication principle of counting, which states that if we have m ways of doing one thing and n ways of doing another, then we have m x n ways of doing both things together.

Using this principle, we can find the total number of ways of going from A to B and returning as follows:

- First, we find the number of ways of going from A to B, which is 6, since there are 6 different routes.
- Next, we find the number of ways of returning from B to A, which is also 6, since we can choose any of the 6 routes for returning.
- Finally, we apply the multiplication principle to find the total number of ways of going from A to B and returning, which is 6 x 6 = 36.

Therefore, there are 36 different ways in which we can go from station A to station B and return, given that we can choose any of the 6 routes for returning.

6×6